They have the right to live, and the state attorney knows that (the law) allows them to defend their lives.

Bali Nine pair's lawyer, Leonard Arpan

However, the president's legal team argued his clemency power could not be contested and the court did not have the authority.

In their verdict, the judges dismissed expert witness testimony provided by Mr Widodo's lawyers because they did not appear in person.

"There is no more legal recourse," Novarida, head of the state lawyers team, told reporters after the decision.

Lawyers for the pair said they were disappointed in the verdict and vowed to continue to pursue all legal options to save Chan and Sukumaran.

"They have the right to live, and the state attorney knows that [the law] allows them to defend their lives," the pair's lawyer Leonard Arpan told reporters.

Chan and Sukumaran resilient, in good spirits: lawyer

Peter Morrissey SC, who is part of the team of lawyers that has been exploring every legal avenue to spare the two Australians, told Lateline the pair may not hear the result until Tuesday, citing their location on Nusakambangan island as the reason for the delay.

He said the pair would be disappointed with the result, but were resilient and in good spirits.

"Of course it's a pretty stressful situation. They will be disappointed when they're told of the result," he said.

"They're resilient. They take blows like this all the time and they remain lovely people ... they are good, strong people.

"They know that there was a chance of winning and a chance of losing ... they're also aware that we're going to keep fighting," he said.

Legal team to appeal to Indonesia's constitutional court

Another of the pair's lawyers, Michael O'Connell, said in the next few days the pair's Indonesian legal team would lodge an application in Indonesia's constitutional court.

"That application is essentially directed to the way in which the clemency law should be interpreted," he told the ABC.

Both men have undergone extensive rehabilitation and I will continue to make representations to my counterpart, just as Australia will continue to use all diplomatic options to seek a stay of execution.

Julie Bishop, Foreign Affairs Minister

"It argues that there should be an obligation on the president to genuinely consider the clemency application."

Mr O'Connell said the judges' decision, however, came as a surprise.

"Whilst there's a constitutional power for the president to grant clemency, that power is regulated by statute," he said.

"The application [in the administrative court] was really directed to the law that regulates clemency rather than the constitutional power."

In a statement, Foreign Affairs Minister Julie Bishop said the Australian Government was disappointed with the decision.

"Both men have undergone extensive rehabilitation and I will continue to make representations to my counterpart, just as Australia will continue to use all diplomatic options to seek a stay of execution," she said.

Opposition Leader Bill Shorten and Opposition spokeswoman for foreign affairs Tanya Plibersek said all legal processes should be allowed to run their course.

"While there's life, there's hope," they said in a joint statement.

"We will not give up. We continue to offer every support to the Australian Government in relation to this matter."

The court's ruling against Chan and Sukumaran does not mean they will face a firing squad straight away.

The two are among 10 drug convicts awaiting execution on Nusakambangan island prison, but the Indonesian government is waiting for all of those listed for execution alongside them to exhaust all legal avenues of appeal.

How long that could take is still unclear.

Jakarta has said it will wait for all legal appeals to be resolved before putting the group to death at the same time. Some other convicts have lodged Supreme Court appeals, which could take weeks to resolve.

Indonesia originally planned to carry out the executions in February, but, following an international outcry, agreed to let legal appeals run their course.